Reserach Notes

Added file	Description
vqa_matlab.m	Matrix implementation of gates to verify equations used in the paper
classical_poisson.ipynb	Notebook with FDM solution of implemented VQA, validates the physics solved by quantum algorithm

Original README below

Variational quantum algorithm based on the minimum potential energy for solving the Poisson equation

This codes solves the one-dimensional Poisson equation based on the variational quantum algorithm.

Requirement

Software	Version
python	3.7.4
qiskit	0.23.6
qiskit-aer	0.7.5
qiskit-aqua	0.8.2
numpy	1.19.1
scipy	1.6.1

To run jupyter notebook,

Software	Version
matplotlib	3.4.2
tqdm	4.60.0

Usage

See sample.ipynb as a sample code.

from vqa_poisson import VQAforPoisson

num_qubits = ... # int
num_layers = ... # int
bc = ... # str
oracle_f = ... # qiskit.QuantumCircuit
qins = ... # qiskit.aqua.QuantumInstance
vqa = VQAforPoisson(num_qubits, num_layers, bc, oracle_f=oracle_f, qinstance=qins)
x0 = ... # numpy.ndarray
res = vqa.minimize(x0)

Citing the library

If you find it useful to use this module in your research, please cite the following paper.

Yuki Sato, Ruho Kondo, Satoshi Koide, Hideki Takamatsu, and Nobuyuki Imoto, Variational quantum algorithm based on the minimum potential energy for solving the Poisson equation, Physical Review A, 104: 052409, 2021.

In bibtex format:

@article{sato2021vqa,
  author  = {Sato, Yuki and Kondo, Ruho and Koide, Satoshi and Takamatsu, Hideki and Imoto, Nobuyuki},
  title   = {Variational quantum algorithm based on the minimum potential energy for solving the Poisson equation},
  journal = {Physical Review A},
  year    = {2021},
  volume  = {104},
  issue   = {5},
  pages   = {052409},
}

License

This project is licensed under the Apache License Version 2.0 - see the LICENSE.txt file for details